UPSC CDS I 2025 Mathematics Paper

The initial mixture contains kerosene and turpentine oil in the ratio 3:2.
Total mixture =100L
Kerosene =(3∕5)×100=60L
Turpentine oil =(2∕5)×100=40L
Final kerosene percentage =20%
Formula used:
Final kerosene in the mixture = Total mixture ×( Final kerosene percentage ∕100)
Additional kerosene to be added = Final kerosene - Initial kerosene
Calculation:
Let the additional kerosene to be added =xL.
Total mixture after adding kerosene =100+xL
Kerosene in the new mixture =60+xL
For 20% kerosene in the final mixture:
‌⇒(60+x)∕(100+x)=20∕100
‌⇒(60+x)=(20∕100)×(100+x)
‌⇒60+x=20×(100+x)∕100
‌⇒60+x=(2000+20x)∕100
‌⇒100(60+x)=2000+20x
‌⇒6000+100x=2000+20x
‌⇒6000−2000=20x−100x
‌⇒4000=−80x
‌⇒x=−4000∕80
‌⇒x=−50